Quasi linear representation of the isotropic scattering source for the method of characteristics

C. Rabiti, G. Palmiotti, W. S. Yang, M. A. Smith, D. Kaushik, A. B. Wollaber

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

The Method Of Characteristics (MOC) has been widely used for two dimensional lattice calculations. One of the main drawbacks of the MOC is its poor spatial representation of the within-group energy source, which requires the use of a very fine mesh to adequately resolve the neutron flux solution. The most straightforward way to improve the spatial representation of this source would be to project the scalar flux to a set of higher-order trial functions within each mesh element, but this is expensive. An alternative to this has already been proposed that exploits the angular flux moments on the surfaces of each mesh element. In this paper, we present a new alternative in which we define a higher order representation of the isotropic source. The key feature of our method is the introduction of a new, linear discontinuous source representation that does not resort to an expensive spatial projection. This is accomplished by using a P1 approximation to construct the average derivative of the spatial source. So far, the derivation has been done only for a linear representation of the isotropic sources in two and three-dimensional geometries. The paper presents an analysis of the performance of the new method in simple cases and the Takeda 1 benchmarks.

Original languageEnglish
Title of host publicationAmerican Nuclear Society - International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009
Pages461-473
Number of pages13
Volume1
Publication statusPublished - 2009
Externally publishedYes
EventInternational Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009 - Saratoga Springs, NY, United States
Duration: 3 May 20097 May 2009

Other

OtherInternational Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009
CountryUnited States
CitySaratoga Springs, NY
Period3/5/097/5/09

Fingerprint

method of characteristics
Linear Representation
Method of Characteristics
Scattering
Fluxes
Neutron flux
mesh
scattering
Mesh
Derivatives
Geometry
Higher Order
energy sources
flux (rate)
Alternatives
Neutron
derivation
projection
Resolve
scalars

Keywords

  • Linear source
  • Method of Characteristics
  • Neutron transport

ASJC Scopus subject areas

  • Nuclear Energy and Engineering
  • Computational Mathematics
  • Nuclear and High Energy Physics

Cite this

Rabiti, C., Palmiotti, G., Yang, W. S., Smith, M. A., Kaushik, D., & Wollaber, A. B. (2009). Quasi linear representation of the isotropic scattering source for the method of characteristics. In American Nuclear Society - International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009 (Vol. 1, pp. 461-473)

Quasi linear representation of the isotropic scattering source for the method of characteristics. / Rabiti, C.; Palmiotti, G.; Yang, W. S.; Smith, M. A.; Kaushik, D.; Wollaber, A. B.

American Nuclear Society - International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009. Vol. 1 2009. p. 461-473.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Rabiti, C, Palmiotti, G, Yang, WS, Smith, MA, Kaushik, D & Wollaber, AB 2009, Quasi linear representation of the isotropic scattering source for the method of characteristics. in American Nuclear Society - International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009. vol. 1, pp. 461-473, International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009, Saratoga Springs, NY, United States, 3/5/09.
Rabiti C, Palmiotti G, Yang WS, Smith MA, Kaushik D, Wollaber AB. Quasi linear representation of the isotropic scattering source for the method of characteristics. In American Nuclear Society - International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009. Vol. 1. 2009. p. 461-473
Rabiti, C. ; Palmiotti, G. ; Yang, W. S. ; Smith, M. A. ; Kaushik, D. ; Wollaber, A. B. / Quasi linear representation of the isotropic scattering source for the method of characteristics. American Nuclear Society - International Conference on Mathematics, Computational Methods and Reactor Physics 2009, M and C 2009. Vol. 1 2009. pp. 461-473
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AB - The Method Of Characteristics (MOC) has been widely used for two dimensional lattice calculations. One of the main drawbacks of the MOC is its poor spatial representation of the within-group energy source, which requires the use of a very fine mesh to adequately resolve the neutron flux solution. The most straightforward way to improve the spatial representation of this source would be to project the scalar flux to a set of higher-order trial functions within each mesh element, but this is expensive. An alternative to this has already been proposed that exploits the angular flux moments on the surfaces of each mesh element. In this paper, we present a new alternative in which we define a higher order representation of the isotropic source. The key feature of our method is the introduction of a new, linear discontinuous source representation that does not resort to an expensive spatial projection. This is accomplished by using a P1 approximation to construct the average derivative of the spatial source. So far, the derivation has been done only for a linear representation of the isotropic sources in two and three-dimensional geometries. The paper presents an analysis of the performance of the new method in simple cases and the Takeda 1 benchmarks.

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